Concentration Dependence of the Range of Spin Polarization in Pd(Fe) AlloysD. J. Kim and Brian B. Schwartz Citation: Journal of Applied Physics 40, 1208 (1969); doi: 10.1063/1.1657590 View online: http://dx.doi.org/10.1063/1.1657590 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/40/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Ferromagnetic transition in PdFe and PdCo alloys (abstract) J. Appl. Phys. 61, 4255 (1987); 10.1063/1.338491 Magnetostriction of PdFe alloys J. Appl. Phys. 55, 1073 (1984); 10.1063/1.333190 Magnetoresistance of PdFe and PdNiFe alloys J. Appl. Phys. 54, 1887 (1983); 10.1063/1.332242 Fe Hyperfine Fields in Dilute Pd–Fe Alloys J. Appl. Phys. 39, 965 (1968); 10.1063/1.1656345 Magnetic Properties of Pd–Fe Alloys J. Appl. Phys. 39, 960 (1968); 10.1063/1.1656342

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1208 DOCLO, FONER, AND NARATH

attained for x(T) within the present resolution of the band calculations. However, it is clear that a factor of two or more increased resolution of the present band calculations would permit us to examine the applica­bility of these models in detail. Hopefully these cal­culations will be forthcoming soon.

We are grateful to B. B. Schwartz, D. J. Kim, A. Misetich, H. C. Praddaude, and F. M. Mueller (Ar­gonne National Laboratories) for many useful dis­cussions, and to 1. De Grave, E. J. McNiff, Jr., and D. C. Barham (Sandia Laboratories) for their assistance with the experiments.

JOURNAL OF APPLIED PHYSICS VOLUME 40, NUMBER 3 1 MARCH 1969

Concentration Dependence of the Range of Spin Polarization in Pd(Fe) Alloys D. J. KIM AND BRIAN B. SCHWARTZ

Francis Bitter National Magnet Laboratory,* Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

According to recent neutron-scattering experiments of Low and Holden, the conduction-electron spin polarization around a magnetic Fe impurity in Pd has a very long range ",lOA. This long range has been attributed to the large exchange enhancement in Pd. Another interesting aspect of this problem, although it has received less attention, is that the range of the spin polarization, the total giant moment per impurity atom, and the Pd high-field susceptibility depend very sensitively on the concentration of the magnetic impurity. For example, neutron scattering shows that an increase in the Fe concentratioa from 0.26% to only 4.0% reduces the range from 10 to 1 A. We understand this very sharp dependence of the range by taking into account the increase in spin splitting of the host Pd bands with increasing Fe concentration. The expression for the q-dependent susceptihlltty for split bands is generalized to include the effects of the detailed structure of electron interactions and is used to obtain a quantitative fit to the data.

According to the recent neutron-scattering experi­ment of Low and Holdenl the conduction-electron spin polarization around a magnetic impurity such as Fe or Co in Pd has a very long range, ,....,10 A. This ex­ceedingly long range of magnetic perturbation due to a magnetic impurity in Pd is attributed to the large spin magnetic susceptibility of Pd metal. Recently, in attempting to reproduce the neutron-scattering data of Pd(Fe) fully quantitatively, Clogston2 noted the im­portance of the interatomic, besides the intra-atomic, electron interaction in Pd. Another interesting aspect of the problem, although it has received less attention, is that the range of conduction electron spin polarization around a magnetic impurity depends very sensitively on the concentration of the magnetic impurity, i.e., the neutron-scattering experiment shows that by in­creasing Fe concentration from 0.26 to 4.0 at. % the range reduces from 10 to 1 A. A similar situation is observed in the rapid decrease of the magnitude of the giant moment and the high-field Pd susceptibility with increasing Fe concentration. In this paper we are pri­marily interested in this problem of the concentration dependence of the conduction-electron spin polarization around a magnetic impurity as observed by neutron scattering.

* Supported by the U.S. Air Force Office of Scientific Research. 1 G. G. Low and T. M. Holden. Proc. Phys. Soc. 89, 119 (1966);

T. J. Hicks, T. M. Holden. and G. G. Low, J. Phys. C (Proc. Phys. Soc.) Ser. 2, 1,528 (1968); J. W. Cable, E. O. Wollan, and W. C. Koehler, Phys. Rev. 138A, 755 (1965).

IA. M. Clogston, Phys. Rev. Letters 19, 583 (1967).

To present the analysis of the Pd(Fe) system, we start with a finite number of magnetic Fe impurities and calculate the q-dependent conduction-electron spin polarization (O'0(q) > using the two-time Green's func­tion technique. In the ferromagnetic state of sufficiently concentrated Pd(Fe) alloys, the conduction-electron bands of Pd are spin split as in ordinary ferromagnetic metals such as Fe and Ni. A simplified form obtained for (O'0(q), (q~O), assuming the spins are ferromag­netically ordered along the z axis, is3 ,4

(0'2(q)= [!lJ(q) /NJ(S2(q) >

X x~ *(q) +xo-*(q) +2U(q)x~ * (q)xQ-*(q) (1) 1-U(q)2x~*(q)xQ-*(q) ,

where xo.r*(q) = xo.-(q) [1-JJ(q)xo.r(q) ]-1 (0'=+ or -). In Eq. (1) the bands of the conduction electrons of the host metal are approximated by the same l-fold degenerate band, J(q) is the s-d exchange integral, N is the total number of atoms in the system,

S«q) = L: So" exp(iqRi), •

where S. is the impurity Fe spin at the lattice point R i ,

Xo.r(q) = - L: (/","-/k+9.,") (€k, .. -Ek+q,,,)-l k

aT. Izuyama, D. J. Kim, and R. Kubo, J. Phys. Soc. Japan 18, 1025 (1963); D. J. Kim and B. B. Schwartz, Phys. Rev. Letters 20, 201 (1968).

4 D. J. Kim and B. B. Schwartz, Phys. Rev. Letters 21, 1744 (1968), and (to be published).

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RANGE OF SPIN POLARIZATION IN Pd(Fe) ALLOYS 1209

is the unenhanced longitudinal spin susceptibility where

jk±= (exp{,8[~k=t=(l/N)J<Sz(o»

+ U(O)n± -.g(O)n±-,uJI + 1)-1, (2)

U(q) is the Fourier component of the electron inter­action (Coulomb repUlsion) between electrons of opposite spins including the intra- and interatomic and intra- and interband components, and .g(q) is the elec­tron interaction (exchange minus Coulomb) between electrons of parallel spins, again including intra- and interatomic and intra- and interband components, n" is .the number of conduction electrons with spin u, and }J. is the chemical potential. An important point to note about Eq. (1) is that XIl<r or XIl<r* is a function of the uniformly spin-split Fermi distribution function jk". The fact that the more concentrated Pd(Fe) system is ferromagnetic and the conduction electron bands are spin split has not been taken into account properly in the usual formulation of the spin polarization problem where only a single impurity is introduced in the Pd matrix.

The elastic diffuse neutron-scattering cross section5,6

measured by Low and Holden is given as'

du/dfJ.= ('Yf?/m0e2) 2 (1-k.2) (Sz)2No

X[1+(u z(q)/(sz(q»]2(1- L~q,K), (3) K

where in Eq. (3) the average is taken over a random distribution of impurities, K is 0 or the reciprocal lattice vector, and No is the number of impurities.

To analyze the actual experimental data on the neutron scattering on Pd(Fe) alloys we adopt these additional simplifications: We assume three equally occupied parabolic d bands (corresponding to the three nonequivalent X points) with the total number of holes per atom equal to 0.36 yielding kF=0.62X 108 cm-I •2,7

J(q) is set equal to zero, since the magnitudes of the Coulomb and exchange integrals between electrons of the same spin with the same orbitals are approximately ~qual. T~us XIl<r*(q) in Eq. (1) is simply XIl<r(q). U(q) is approXlmated by a Lorentzian U(q) = U(O) (1 + Bq2/ 12kF2)-1, where B is chosen to fit the observed q depend­~nc: of the nt;utron scattering in the single impurity limit and remams constant for the spin-split calculations.

All the parameters appearing in Eqs. (1) and (3) can be obtained from experimental data and are es-

: G. G. Low and M. F. Collins, J. AppJ. Phys. 34, 1195 (1963). W. Marshall, J. Phys. Chern. (Proc. Phys Soc) Ser 2 1 88

(1968). . . .,' ? J. J. Vuillemin and M. G. Priestley, Phys. Rev. Letters 14,

307 (1965); A. J. Freeman, A. M. Furdyna, and J. O. Dimmock J. Appl. Phys. 37,1256 (1966). '

FIG. 1. The dots are the neutron-scattering data obtained by Low and Holden. The solid lines are a theoretical fit. The lowest curve was fit by assuming M=O and B=12 (see text). The M value in parentheses represents the effective magnetiza­tion necessary to repro­duce the data point~.

C~40% (M~I) _._.~ •.• _._._._._ .. _.-::.I.O

-------- :.0 ~ '_._. C~2 2%(M~85~ ~ 1.0 - - --'---.!.-. __ . 5.0

~ 0 ---- - ---- 40 :0- I ~ 70 - _ ] 3.0 a:: " i:! 6.0 "'" C~1.0%(M~.4)12.0 U) ",,--,---

z 5.0 '-'-'-,_. 1.0 a:: ;il 4.0 • 0

10i-o I ___ ~ __ _L._----"

o 0.5 1.0 SCATTERING WAVE NUMBER A"

timated as follows8 : J(O) =0.15 eV, S=!, N(O) U(O) = 0.9, where N(O) =m*kF/27?-1i2 is the density of states of each of the three d bands of Pd at the Fermi surface, the total moment per Fe atom in the low impurity limit is approximated as 10 ,uB.9,IO

In Fig. 1 the dots are the data observed by Low and Holden. ~here is a very sharp change in the scattering cross sectlOn as the Fe concentration increases from 0.26% to 4.0%. The solid line in Fig. 1 represents our theoretical fit using Eq. (3) with the magnetization M= (n+-n_)/(n++n_) or spin splitting of the host Pd band as an adjustable parameter and reproduces the data quite well. According to this fit, a concentration of 1.0%, 2.2%, and 4.0% Fe in Pd corresponds to an effective magnetization of the Pd spin bands of 0.40, 0.85, and 1.0, respectively. This sharp dependence of the effective Pd magnetization with c, however, is about twice as rapid as that which would be calculated from Eq. (2) and is observed experimentally.9 It is not surprising that the effective magnetization and the observed magnetization do not agree exactly since the real Pd. bands can be quite different from the simple parabolic bands we have used in our calculation.

Note added in proof: In Ref. 4 we showed that a smaller value for kj = 0.5 X 108 cm-1 with the same N (0) can remove the quantitative discrepancy of the con­centration dependence of the neutron scattering. This smaller value of kj gives a larger slope in the density of states at the Fermi surface and agrees with recent band calculations.

8 See, for instance, D. J. Kim, Phys. Rev. 149, 434 (1966)' S. Doniach and E. p, Wohlfarth, Proc. Roy. Soc. (London) A296,442 (1967).

~ J; Crangle, Phil. Mag. 5, 335 (1960); S. Foner (to be publIshed).

10 A. M. Clogston and T. H. Geballe (to be published).

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